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transformed into discrete elements if data are to be applied and numerical results obtained.) The importance of the Net Reproduction Rate, defined as a girl child's expected number of girl children, is that it is equal to the ratio of the population in one generation to the population in the preceding generation implied by a given regime of births and deaths.
The Net Reproduction Rate, being a replacement index, combines fertility with mortality up to the end of the reproductive period. A measure of pure fertility is given by the conditional expectation, known as the Gross Reproduction Rate,
GRR = f m(d)da = 5 2 F
n                                n          '
the number of girl children by which the girl child would be replaced if she lived through the reproductive period and was subject to the given age-specific rates of childbearing.
A measure of pure survivorship relevant to childbearing is the ratio of the NRR to the GRR; this was 0.57 in Sweden of 1800 and 0.86 in Honduras of 1966. The probability of a girl child living to reproduce is more than half as high again in Honduras.
Any model of birth, death, and replacement can be applied to males as well, since each boy child has a father just as surely as each girl child has a mother. The female model seems more natural because (a) the data on child-bearing by age of mother are more widely available than births by age of father; (b) the range of ages within which women can be mothers is narrower than the range of ages within which men can be fathers; (c) the number of children that can be bom to a woman is more limited than the number that can be born to a man. Nonetheless we will later use the one-sex model for males.
Now our subject of linkages requires an investigation of how the Net and Gross Reproduction Rates would respond to changes in birth and death rates. The GRR is simpler: it is unaffected by mortality, and a change in an age-specific fertility rate will make an equal change in the GRR. The United States had a GRR of 1.336 in 1966; the average woman who lives through the child-bearing period has approximately 1.336 girls, and about 1.049 times as many boys, or about 2.736 children altogether, at the rates of 1966. Disregarding differences in fertility of those few women who die before the end of their childbearing period, this is the average completed family implied by 1966 age-specific rates. The rate of childbearing to women of 35 to 39 was 0.0206, among the lowest in the world. American women prefer to bear their children early; they bear enough children before age 35 to provide a Gross Reproduction Rate and even a Net Reproduction Rate of more than unity.ife or lives saved may be supposed the result of a durable improvement in medical technique, then we want to know the effect on populations of theage by 2.42 years in comparison with Sweden 1800—evidently the survivorship of Honduras was espe-ion Change on the Attainment of Educa-bout 20 percent. For the less developedHilton Salhanick has observed that some women practicing the rhythm method will break or lose their thermometers at the critical juncture in theirright, therefore alwayshas some c